Lee Disc Setup (easy Mode)

The environmental impact of traditional insulation materials, such as fiberglass and foam plastics raises the need to look for eco-friendly alternatives.

Mycelium shows potential as a renewable and biodegradable insulation material. It requires minimal energy during production and can be cultivated using agricultural waste or organic materials.

Mycelium can be grown on any fibrous organic material, this allows it to be grown on locally sourced waste streams, cutting down on costs and making it a more versatile product. Since the qualities of mycelium largely depend on the substrate it is grown on would be of great value if the thermal conductivity of the mycelium could be measured in a simple, cheap way.

Most of the knowledge came from this website https://thermtest.com/thermal-resources/build-your-own/lees-disc.

This was done as a project for school, the complete report can be found in the appendices.

The most interesting part of this report was the finding that when stacked with the heating element on top, the resulting k values was almost precisely double the k values expected.

·        Two DS18B20 temperature sensors.

·        Two metal discs 50mm by 12mm, use a good conductor, I used aluminum.

·        An insulator to be wrapped around the metal discs, I used rubber I had laying around.

·        An Arduino.

·        A hot plate, I used this one. https://www.amazon.nl/gp/product/B08K8ZDJKL/ref=ox_sc_act_title_1?smid=A3BYGDRTULI6GE&psc=1

·        A sample to be measured.

·        A terminal block.

·        Power cable for wall sockets.

To plot the sensor data I used LabVIEW, if you do not have access to LabVIEW find an alternative method.

I used a 3D printer, if you are resourceful enough you can do without.

I’m no expert so feel free to take a different approach with different components.

Drill holes for the sensors in the discs. Not all the way through.

Glue the insulation material to the sides of the metal discs, make a hole to stick the sensor through.

Make a housing for the heating element so you can handle it without getting burned.

Connect the heating element to the power cable using terminal blocks.

Make a stand to hold the discs, make sure to have as little contact area as possible.

Wire the sensors to the Arduino.

Program the Arduino to read the sensors and send their data over Serial.

#include <OneWire.h>
#include <DallasTemperature.h>


#define TS1_pin 4
#define TS2_pin 3


float T1;
float T2;


// Setup a oneWire instance to communicate with any OneWire devices
OneWire oneWireTS1(TS1_pin);
OneWire oneWireTS2(TS2_pin);


// Pass our oneWire reference to Dallas Temperature sensor
DallasTemperature TS1(&oneWireTS1);
DallasTemperature TS2(&oneWireTS2);


void setup(void) {
  // Start serial communication for debugging purposes
  Serial.begin(9600);
  // Start up the library
  TS1.begin();
  TS2.begin();
}


void loop(void) {
  // Call sensors.requestTemperatures() to issue a global temperature and Requests to all devices on the bus
  TS1.requestTemperatures();
  T1 = TS1.getTempCByIndex(0);
  TS2.requestTemperatures();
  T2 = TS2.getTempCByIndex(0);
  Serial.print(T1);
  Serial.print(",");
  Serial.println(T2);
  delay(1000);
}

Make this LabVIEW block diagram to read serial and plot the data.

In my program, the sensor data sometimes spikes up or down, this is most likely caused by a Serial read error. Since I could still do the measurement with these spikes, I did not bother to fix it.

Stack the components like this.

Heat the stack until steady state is reached, steady state is reached when the temperature does not change for around 5 minutes. The accuracy of the sensors is 0.5 °C so these jumps can be ignored.

Record T1 and T2 at steady state.

Once steady state is reached, heat only the bottom metal disc like this.

Heat the metal disc to about 5 °C above its steady state temperature.

Remove the heating element and place the measured insulator on top of the metal disc.

My results are better when weighing down the insulator with something, here i used a coffee cup.

Allow the metal disc to cool to about 5 °C below its steady state temperature.

Calculate the slope of the cooling curve at the SS temperature of the bottom disc.

The Rate of heat transfer at steady state through a given material is given by the following equation.

Q = k ⋅ A ⋅ (T₁ – T₂) / d       (1)

The rate of cooling of at steady state temperature is given by the following equation.

Q = m ⋅ c ⋅ (dT/dt)            (2)

Since at steady state, the amount of heat entering a system is the same as the amount of heat leaving a system, the following equation may be produced.

K ⋅ A ⋅ (T₁ – T₂) /d = m ⋅ c ⋅ (dT/dt)               (3)

The Thermal Conductivity constant may be isolated to produce the following.

K = [m ⋅ c ⋅ (dT/dt) ⋅ d] / A ⋅ (T₁ – T₂)            (4)

With

·        k = Thermal Conductivity in Watts/meter-Kelvin

·        A = Area (m²)

·        T₁ and T₂ = Temperatures in °C

·        d = Thickness of the sample

·        m = mass of one metal disc

·        c = specific heat of the material of the discs in Joules/Kilogram-Kelvin

·        (dT/dt) = Rate of cooling in °C/Second

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